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Summary: Points and Combinatorics
Oswin Aichholzer, Franz Aurenhammer, Hannes Krasser
Institute for Theoretical Computer Science
Graz University of Technology
Graz, Austria
e-mail: foaich,auren,hkrasserg@igi.tu-graz.ac.at
Which point sets exist, anyway?
This intuitive question sketches the topic of the article
at hands. Its relevance is apparent: a con guration of
n points is the underlying structure for countless prob-
lems in computational and combinatorial geometry.
In fact, a point set in the Euclidean plane is among
the simplest geometric objects that lead to non-trivial
questions { in a geometrical, combinatorial, and algo-
rithmic sense. Not surprisingly, most basic data struc-
tures in computational geometry have rst been devel-
oped for point sets, and have been later generalized to
more general objects, like line segments, circles, poly-
gons, etc. Examples include geometric search trees,
convex hulls, Voronoi diagrams (an accompaning ar-
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